Determination of Undercutting Avoidance for Designing the Production Technology of Worm Gear Drives with a Curved Profile

Abstract

One of the most difficult production geometry tasks arising in the machining process of the elements of a drive pair is to avoid undercuts. It is a serious technological challenge to determine the production of the elements of worm gear drives avoiding the phenomenon undercut, especially in the case of a pair consisting of a curved profile worm and its mating wheel. The technology of forming the tooth surface requires a separate examination in each case, running the simulation procedure of the tool geometry and the movement conditions when forming different teeth. This article proposes a new concept for determining and then avoiding the positions of undercutting by examining the patented worm with a circular arc profile in axial section, due to its extremely advantageous aspect in terms of production technology. The cutting edge of the hob, formed from the substitutional worm, moves on the tooth surface of the worm, and produces the tooth surface of the conjugate wheel. The gear tooth surface has been determined based on the main law of gearing with the lines consisting of the contact points of the conjugated surfaces. The conditions for the disappearance of the common normal or the relative velocity fitting to the common tangent plane of the contacting points are defined in this paper.